In a Couette flow, two large flat plates lie one on top of

QUESTION:

In a Couette flow, two large flat plates lie one on top of another, separated by a thin layer of fluid. If a shear stress is applied to the top plate, the viscosity of the fluid produces motion in the bottom plate as well. The velocity V in the top plate relative to the bottom plate is given by \(V=\tau h / \mu\), where \(\tau\) is the shear stress applied to the top plate, h is the thickness of the fluid layer, and \(\mu\) is the viscosity of the fluid. Assume that \(\mu=1.49 \mathrm {\ P a \cdot s}\) and \(h=10 \mathrm{~mm}\), both with negligible uncertainty.

a. Suppose that \(\tau=30.0 \pm 0.1\ \mathrm{P a}\). Estimate V, and find the uncertainty in the estimate.

b. If it is desired to estimate V with an uncertainty of 0.2 mm/s, what must be the uncertainty in \(\tau\) ?

Equation Transcription:

Text Transcription:

V={tau}h/mu

tau

mu

mu=1.49 Pa{cdot}s

h=10 mm

tau=30.0{+/-}0.1 Pa

0.2 mm/s

tau